Add djordon's security proof to white paper #93
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djordon
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djordon
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Oct 27, 2024
| = \sum_{i \in S}^{} d_{i} + \rho_{i} \cdot e_{i} + c \cdot \sum_{k \in K_i}^{} \lambda_{k} \cdot s_{k} | ||
| \end{align} | ||
| %% | ||
| where $S$ is the signing set, $d_i$ and $e_i$ are private nonces, $K_i$ is the key ID set for participant $i$, $\rho_i$ is a hash of the message with identifier $i$ and the nonces \eqref{equation:message-participant-hash}, and $c$ is a hash of the message with the public key \eqref{equation:message-public-key-hash}. Luckily, equation \eqref{equation:signature-wsts-appendix} tells us who to include in the signature on the FROST side to generate the same signature. Specifically, we select the participants in $S$, along with the dummy participants identified by the key IDs in $\bigcup_{i \in S} K_i$. These dummy participants do not contribute to the $\sum_{i \in S}^{} d_{i} + \rho_{i} \cdot e_{i}$ portion of the signature in \eqref{equation:signature-wsts-appendix}, since their private nonces are zero. Thus the FROST signature is: |
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